Can't update AT&t NOTE 2 while using tmobile sim card?

MY sister has an att galaxy note 2. She've since left att and switched to tmobile. She also got att to unlock the phone before she left so she could use her tmobile sim card.

Now i'm trying to update her note 2 from 4.1.2 to 4.3 or 4.4 and it says there are no servers or updates avaiable. So you can't update an att note 2 while on tmobile network?
Also if i'm somehow able to do it, would updating her phone lock her phone again and prevent her from using her tmobile sim card?

Would flashing any roms also lock the phone and prevent using tmobile sim?